stats op• Data kinds: matrix → matrix
• Call: import fullseye as fs; fs.ledger.stat_covariance(x) (to call the implementation directly, import mathops; mathops.stat_covariance(x); from the registry, opsmath.get("stat_covariance"))
Sample covariance matrix of (N, D) observations → (D, D).
Rows are observations, columns are variables — the (N, D) orientation every Fullseye point/sample API uses (note np.cov defaults to the *transposed* convention). Uses the unbiased ddof=1 estimator (divides by N - 1), hence the N >= 2 requirement. The diagonal holds the per-variable sample variances; the result is symmetric positive semi-definite by construction, so it can go straight into mat_eigh for principal axes (the covariance-ellipse workflow).
HALCON: no public tuple/matrix operator — covariance lives inside HALCON's calibration and matching internals only.
Every mathops op validates its input before computing (nothing slips through silently):
• complex input raises ValueError — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• masked arrays with masked elements raise ValueError — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• NaN/Inf raises ValueError on every input (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• measurement_uncertainty — Measurement uncertainty and calibration — what it takes to claim you are measuring
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• math_metrology — py -3.11 examples/math_metrology.py
• poc_thermal_radiometry — py -3.11 examples/poc_thermal_radiometry.py
matrix as input)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond · mat_lu · mat_qr
stats)stat_describe · stat_histogram · stat_correlation · stat_zscore
*Provenance: mathops.py — MATH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.